A tangent PQ at a point P of a circle of radius 5 cm meets a line through the centre O at a point Q such that OQ = 12 cm. Length PQ is cm

Question

Philoid · Accepted Answer

Given:

OQ = 12 cm

Property: The tangent at a point on a circle is at right angles to the radius obtained by joining center and the point of tangency.

By above property, ∆POQ is right-angled at ∠OPQ.

Therefore,

By Pythagoras Theorem in ∆POQ,

OP² + PQ² =OQ²

⇒ PQ² = OQ² – OP²

⇒ PQ= √( OQ² – OP²)

⇒ PQ= √(12² – 5²)

⇒ PQ= √(144 – 25)

⇒ PQ = √119 cm

Hence, PQ = √119 cm